On the track, "Open Letter," Jay-Z — born Shawn Carter — addresses politicians at large and appears to suggest President Obama approved his trip, despite America's long-standing trade embargo with the communist island.

During a "Today" show appearance, Obama denied any involvement in the trip.

"I wasn't familiar that they were taking the trip," the president said on "Today." "My understanding is I think they went through a group that organizes these educational trips down to Cuba. You know, this is not something the White House was involved with. We've got better things to do."

Though travel restrictions have eased under President Obama for academic, religious or cultural exchanges, U.S. residents typically are required to have a government-granted license to visit Cuba.

The trip garnered almost immediate backlash from some Republican lawmakers as pictures of the couple rushed by locals, posing with area schoolchildren and dining at the renowned restaurant La Guarida, flooded the internet.

Republican lawmakers from Florida who represent areas with strong Cuban-American populations, including Sen. Marco Rubio, questioned what type of license the couple acquired to make the trip. It was later confirmed by the U.S. Treasury Department that the trip was sanctioned.

Rubio accused the Obama administration of not doing enough to enforce the travel ban.